Mathematics Courses Research Articles

METHODOLOGY OF TEACHING ELEMENTS OF COMBINATORICS AT THE COMPREHENSIVE SECONDARY SCHOOL

The object of the study is the elements of combinatorics at the comprehensive secondary school. The aim of the article is to improve the methodological system of teaching elements of combinatorics at the comprehensive secondary school. The article discusses methodological issues and problems of studying combinatorics elements in the process of teaching mathematics. The methodological features of studying combinatorics elements at the comprehensive secondary school are identified and characterized, their role in the course of mathematics from the point of view of improving the effectiveness of learning is considered. The methods and methodical techniques of teaching combinatorial material, which were previously tested in our educational process, are presented. The possibilities and expediency of their application in connection with the age peculiarities of students are substantiated. Methodological guidelines for teaching individual topics of combinatorics are given. Within the framework of teaching each topic, interesting tasks of applied significance are presented. Effective methods of their solution are given. The presented tasks have been tested for years in our teaching practice. In the process of teaching the elements of combinatorics, methods of cooperative learning, mathematical modeling, graphical modeling, coding, methods that promoting inter- and intra-subject connections were used.

Students' Errors in Constructing Mathematical Proofs by Direct Method

In mathematics, there are several methods for proving mathematical statements, two of them are direct method and indirect method. Both the methods were included in the mathematics curriculum at senior high school level as a learning topic. It implied that the teachers or pre-service teachers must master these methods. In addition, learning advanced mathematics courses also needed the ability of mathematical proving. The direct method was often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to 13 college students. They were pre-service mathematics teachers in one of the public universities in Aceh, Indonesia, and were asked to prove the statements by direct method. The data were analyzed by using Miles and Huberman step. The results showed that there were three main errors, (1) errors in using definition correctly, (2) errors in algebraic process, and (3) proving by examples. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs. Keywords: constructing mathematical proofs, direct method, students’ errors

Perspectives from students and teachers about the challenges of teaching and learning STEM subjects in Ghana

Ghana has recently renewed its commitment to build a strong Science, Technology, and Innovation (STI) base for improved socio-economic development. This commitment hinges on recognizing that the strength of the nation’s STI policy depends on the quality of pre-tertiary education and training in science and mathematics to produce a critical mass of young people well-prepared for Science, Technology, Engineering, and Mathematics (STEM) courses at the tertiary level. However, despite numerous interventions to improve upon STI, Ghana still performs poorly, along with other Sub-Sahara Africa (SSA) countries with common STI indicators in the Global Innovation Index. Using Ghana as a lens, this article highlights the challenges in STEM teaching and learning throughout the sub-region. The qualitative research approach was adopted to allow an in-depth exploration of participants’ perspectives. Six pre-tertiary schools (three Junior High Schools and three Senior High Schools) and the University of Ghana, Legon, were selected due to the availability of their students and teachers to participate in the interviews in Accra, the capital city. This article argues that, to develop the critical mass of human capital needed for sustainable development, there is a need to improve the performance of students in STEM subjects at the pre-tertiary level. In addition, performance improvement, which is linked to student interest in the study of STEM subjects, should increase the quality of students entering tertiary education institutions. These students will then be trained to meet the quality of human resources needed to run the STI system—a step toward achieving sustainable development this article recommends the redesign of STEM curriculum at the pre-tertiary level to align with tertiary STEM education as that in turn aligns with Ghana’s STI system.

Mathematics Anxiety among Architecture Students at Polytechnic Sultan Idris Shah: A Preliminary Study as An Attempt to Strengthen Mathematics Education in TVET Institution

Mathematics is the basis for numerous technical skills imparted in Technical and Vocational Education and Training (TVET) institutes. As one of the TVET institutions, Polytechnic recognizes the importance of mathematics courses in its curriculum. Engineering, computer science, architecture, and manufacturing courses rely heavily on mathematical principles and concepts. Despite the importance of mathematics, the issue of underperformance in Elementary Mathematics courses among architecture students has been a significant issue for Polytechnic institutions. Some architecture students may require assistance understanding the direct applicability of specific mathematical topics to their field of study. They may perceive mathematics courses as arduous, demanding, intricate, and challenging to succeed in. The presence of negative thoughts significantly led to the development of mathematical anxiety. This anxiety can hinder their ability to solve problems and perform to their full potential in mathematics courses. Therefore, this study investigates the correlation between mathematics anxiety and problem-solving skills among architecture students. The study utilizes a quantitative research design, employing a questionnaire and a problem-solving test. This study used convenience sampling to select 45 Diploma in Architecture students who took Elementary Mathematics in semester one. The data collected is analysed using descriptive and correlation analyses. The study results indicated that mathematics anxiety is present among architecture students. Furthermore, a significant negative correlation was observed between mathematics anxiety and the mathematical problem-solving abilities of architecture students enrolled in elementary mathematics courses. It indicates that their abilities to solve mathematical problems decreases as their mathematics anxiety increases. Consequently, mathematics anxiety is a factor that influences the problem-solving abilities of students. Hence, educators must strive to understand mathematics anxiety and implement innovative pedagogical approaches to overcome their anxiety. Ultimately, the insights gained from the research will contribute to the current body of literature concerning mathematics anxiety and its ramifications for problem-solving within architecture education.

Investigating Billingual Education as A Language Framework and Its Application for Successful Social Engagement

Objective: The research reveals the impact of the course on English and English for mathematics conversations, highlighting improvements and identifying challenges in expressing mathematical ideas. Overall, it aims to analyze code-switching types and reasons in the English for Mathematics course context. Method: This qualitative case study explores code-switching in English for Mathematics courses, unveiling the nuanced types employed by lecturers and students during classroom interactions. From tag-switching to intra-sentential and inter-sentential code-switching, the classroom becomes a dynamic linguistic canvas. The study investigates motivations behind this interplay, including internal factors like language proficiency and fear of linguistic missteps, and external influences like participant dynamics and contextual nuances. Research Findings and Discussions: Although this course is due in English, the use of the Indonesian language also happens for both lecturers and students. The occurrences of code-switching itself are on the type of tag switching, intra-sentential, and inter-sentential switching. Internal and external factors influence code-switching in classroom interactions. Internal factors, such as language ability and preferences, impact students' comfort with using specific languages. External factors, including participants, context, and lesson topics, also shape code-switching occurrences in educational settings. Research Implications: The research implied to improve students' English proficiency in mathematics, emphasizing understanding mathematical terms and delivering presentations in English. By implementing the code switching. Originality/Value: This research offers lecturers and students point of views related to the types of code switching used by both of them in the process of teaching and learning as well as it is also reasons for using code switching where it contributes for both of them to understand and master the English for Mathematics Course. Then, this exploration offers insights into the symbiotic relationship between language and subject matter within the English for Mathematics classroom, revealing the vibrant tapestry of this linguistic and educational dynamic.

“I’m a bit out of place here.”—Preservice teachers’ positioning in the figured world of university mathematics

Preservice mathematics teachers are sometimes trained in programs so that they have both their own courses and joint courses with mathematics majors from the beginning of their studies. While this is thought to provide them with both deep mathematical knowledge and teaching-specific content right from the start, many of them report disaffection with and disengagement from mathematics during their very first semester. Current approaches often frame this from an individual’s perspective, investigating cognitive and affective individual differences among students. In contrast, we aim to understand this issue from a sociocultural perspective, examining underlying social processes. In this study, we thus explored preservice teachers’ experiences of the mathematics component of their training, using Holland and colleagues’ theory of figured worlds as a theoretical lens. Three group interviews with 14 preservice higher secondary teachers in a common mixed setting in Germany (one course specific to preservice teachers, one general mathematics course together with major students) were analyzed. Our findings displayed that the preservice teachers experienced two dichotomous figured worlds of mathematics and mathematics teaching. Our further analysis of their positioning between these worlds provided new insights to explain their disaffection, disengagement, and consequent learning behavior. We discuss practical implications, focusing on different teaching systems and interventions in teacher education.

Contextual mathematical tasks as a means of developing students� functional literacy in school mathematics course

Relevance. The relevance of the research is conditioned upon the existence of a contradiction between the predominantly abstract-theoretical nature of the conventional school course of mathematics and the objective need to develop students� skills in the practical application of mathematical knowledge and tools to solve specific applied problems in real-life situations. Purpose. The purpose of the research is to identify and comprehensively justify the role and place of contextual mathematical tasks in the development of students� functional literacy, understood as the ability to apply mathematical knowledge in life situations. Methodology. The study employed methods of historical and comparative analysis, curriculum and educational policy analysis, and the generalization of best practices. Results. The work analyses the historical evolution of advanced national systems of mathematics education from the perspective of integrating the practice-oriented contextual approach into them. It is demonstrated that in many countries there has been a gradual transition to more applied mathematics education through the inclusion of realistic contextual tasks. The high effectiveness of school students solving mathematical problems contextualised in everyday scenarios for developing competence in applying abstract mathematical knowledge and skills in real-life situations has been proved. A set of factors stimulating the introduction of the contextualised approach in mathematics teaching, such as the results of international assessments, has been explored in detail. Conclusions. Key pedagogical, methodological and organisational conditions for the successful implementation of this approach in the school system, including the development of teaching materials, teacher training and assessment tools, are identified. The results expand the understanding of the possibilities of contextual tasks in the development of students� functional literacy, which is significant for the improvement of mathematics education. Keywords: mathematics education; practice-oriented learning; application of knowledge; pedagogical practices; curriculum

Positioned as a burden: Analyzing the participation of multilingual students of color in undergraduate mathematics courses that use groupwork

More college mathematics classrooms are adopting active learning practices like groupwork. These practices typically foreground vocal communication and interpersonal interactions, both of which are mediated by language. Given that undergraduate classrooms in the U.S. are also becoming more racially and linguistically diverse, this study focuses on multilingual students of color, whose learning experiences have often been overlooked. Specifically, this study aims to learn more about the relationship between groupwork and equity in classrooms with linguistic diversity. Using positioning theory, this study analyzes the learning narratives of 26 multilingual students of color about their experiences working with peers in groups. Findings demonstrate that while multilingual students described enacting a range of different positional identities during groupwork, they were more likely to report being positioned by others in deficit ways. Results highlight how the positional identities perceived to be available to students were often constrained by normative classroom Discourses about language, participation, and mathematics.

Development of Basic Mathematics Modules Based on Professional Competencies

The low ability to understand mathematical concepts affects the learning outcomes of information systems study program students in basic mathematics courses. This is because basic mathematics courses tend to be disliked by the YPTK information systems study program students at Putra Indonesia University in Padang. After all, they consider basic mathematics courses do not significantly contribute to their field of expertise. Students prefer courses that suit their area of ​​expertise. Basic mathematics is an abstract subject and is a difficult subject. Students have difficulty applying mathematical concepts to solve problems. The learning module is a basic mathematics module based on professional competence. This basic mathematics module connects basic mathematics subject matter with subject matter in the field of expertise, namely information systems. This research aims to produce a basic mathematics module based on professional competence in the information systems study program at Putra Indonesia University YPTK Padang. This type of research is development research(R&D). The stages in developing this basic mathematics module are the development stages proposed by Plomp. This research carried out a preliminary research stage. Experts carry out product validation. Our instrument is a validation sheet with a Likert scale. The results of the expert validation analysis from aspects of presentation/dictates, suitability of content, language, and graphics obtained an average of 3.39 with a very valid category, which means that the basic mathematics module based on professional competence is suitable for use in basic subjects. Mathematics learning.

Dataset and Development of Learning Analytic Tool to Extract Manifestations of Students’ Agency from Texts of Comments from MOOCs

The study is devoted to the automatic identification of manifestations of various components and sources of student agency from the texts of reviews of MOOCs, as well as descriptions of internal and external transformation among students in the process of studying MOOCs. To extract descriptions corresponding to individual, relational and contextual sources of students’ agency, a dataset of 3445 English-language comments on the most popular mathematics courses presented on the Udemy platform was generated, and additionally 1787 comments on practice-oriented MOOCs and entrepreneurship MOOCs were extracted to understand the descriptions corresponding manifestation of internal and external transformation in MOOC listeners. The paper proposes a methodological approach based on the use of natural language processing methods such as topic modeling, sentiment analysis and N-gram frequency analysis for extracting keywords and their combinations from MOOCs’ comments texts to describe the manifestation of the components of an individual source of student agency in the form of self-efficacy , increased sense of confidence in solving problems and motivation; components of the relational source in the form of support and accompaniment of the online course by the tutor with the help of quick answers and well-structured educational material; components of the contextual source in the form of the ability to make decisions when choosing alternative online courses, as well as descriptions of the manifestation of internal transformation of students, expressed in the transition from internal struggle - overcoming fears, uncertainty, difficulties in perceiving MOOC content to understanding the purpose of learning and external transformation, expressed in the texts of comments on MOOCs in the form of creating a new or changing the structure of an existing product, startup or business through a change in thinking.

The Online Game Design Uses Scratch, Geogebra, and Geogebra AR Through Mathematics Education Multimedia Lectures

This study aims to design online mathematics games using Scratch, Geogebra, and Geogebra AR through multimedia education mathematics courses. This study used the multimedia development life cycle. Participants in the study were 41 students (13 male and 28 female) of fifth-semester in a multimedia course in mathematics education at a university in West Java, Indonesia. The research instrument was a questionnaire through Google Forms, performance appraisal, observation, and interviews. Based on the research results it is known that Scratch, Geogebra, and Geogebra AR can be used in math game design even though previous students have not studied both, but the results are good. The author suggests that students can try out these math games at school during research or teaching practice. In addition, the authors hope that the game can be published on the internet so that it can be used by many students.
 Keywords: game online, scratch, geogebra AR

Students' Perspectives on Selecta Capita of Mathematics Online Course on Their Ability to Develop Mathematics Task

The main problem in implementing online lectures is how to adjust what students expect with the achievement of learning quality. This study examines students’ perspectives on effective lectures on the ability to develop mathematics task. Quantitative descriptive research has been carried out on students of the mathematics education study program Universitas Negeri Semarang who took the Selecta Capita of Mathematics course. The subjects in this study were 101 first-year students in the mathematics education study program at Semarang State University for the 2021/2022 academic year. The data were obtained through questionnaires and analyzed by the descriptive statistics. The data that had been obtained and then tabulated in a table, the average value is searched, and presented in the appropriate graph. The results of the study indicate that the availability of learning modules and videos as learning resources is the most important thing that must be prepared during lectures. Furthermore, several other things such as synchronous lectures, discussions using the WhatsApp Group, the use of the learning management system, group assignments, virtual face-to-face meetings, and project assignments need to be prepared during lectures. These results are needed to be applied on team-based project learning models to develop students’ abilities in developing math tasks.
 Keywords: students’ perspectives, selecta capita, mathematics online course, mathematics task

The Effect of Authentic Learning Activities Used in Mathematic Course on Middle School Students' Academic Achievement and Reasoning Skills

The aim of the study is to determine the effect of activities based on authentic learning approach used in middle school mathematics course on students' academic achievement and reasoning skills. The research covers the learning outcomes of the Whole Numbers, Fractions and Decimal Fractions units in the 6th grade 1st semester of the mathematics course. The implementation of the research was carried out in the first semester of the 2022-2023 academic year in a public school in the Selçuklu district of Konya province. The control and experimental groups consisted of 33 and 26 6th grade students, respectively. The study was conducted for nine weeks in the fall semester. The data of the study were collected with "Academic Achievement Test" and "Reasoning Skills Test". T-test statistics were used to analyze the data. As a result of the study, it was seen that authentic learning activities used in mathematics lessons positively affected students' academic achievement and reasoning skills. These results show that learning experiences close to daily life skills will also contribute to reasoning skills.

Designing a Fund of Assessment Tools in the Structure of an Interactive Course in Higher Mathematics.

Designing a Fund of Assessment Tools in the Structure of an Interactive Course in Higher Mathematics.

Formation and Development of Mathematical Literacy in the Context of PISA-2021 Program Concep

This article presents the results of pedagogical experiments, which revealed educational problems that teachers face in the process of teaching mathematical literacy to schoolchildren: a low proportion of practice-oriented tasks in the total number of educational tasks in school mathematics intended for 15-year-old schoolchildren, a passive attitude of teachers to the formation of mathematical literacy among schoolchildren. The analysis of the experimental data made it possible to conclude that the knowledge and skills of teachers on the issues of reducing the standard task of the school mathematics course are insufficient to problem situations in the context of the PISA assessment tasks, compiling task systems for these tasks, containing an algorithm for solving the assigned problem, description of a visual object that allows the visualization of the task. To solve these problems, the paper proposes to apply a modular learning technology in the process of teaching schoolchildren mathematical literacy, an algorithmic method for reducing a standard task to assessment-learning tasks in the context of the PISA-2021 program concept. In the work, examining the task to the problem situation as an object of mental activity of students, the main components of the "Mathematical Reasoning" of the student are highlighted. Namely: recognizes the area of the task; singles out the main components of the tasks; to bring data under known concepts; establishes interdisciplinary links; applies induction, interdisciplinary knowledge in the preparation of a mathematical model; solves a mathematical problem; interprets, evaluates the solution in the context of the phenomenon under consideration. The analysis of algorithms for solving tasks made it possible to identify the following key structural components of mathematical literacy: understanding the context of tasks; the ability to establish correspondences between various objects, apply induction and knowledge, build mathematical models, find solutions to mathematical models of tasks, interpret and evaluate the solutions obtained; have mathematical reasoning skills. The final experimental study confirmed the effectiveness of the developed methodology for the formation and development of mathematical literacy at 15 year old schoolchildren.

A Research of Activity Related to Convergence Teaching and Learning Methods Using Artificial Intelligence in Advanced Mathematics Courses for Gifted Students

A Research of Activity Related to Convergence Teaching and Learning Methods Using Artificial Intelligence in Advanced Mathematics Courses for Gifted Students

Analysis of students' difficulties in writing skills in English mathematics courses

This research aims to analyze the difficulties faced by students in developing their writing skills in the Mathematics English course. Through a qualitative approach, this research explores the factors that influence student difficulties, including language aspects and mathematical concepts.. The research subjects taken were 5th semester mathematics education students. The data collection methods used were documentation methods, test methods, and observation methods. The documentation method was used to obtain data about the list of names of students who were used as research subjects. The test method is used to obtain data on student completion of English courses, the observation method is used to determine objective conditions during English teaching and learning activities and to determine factors that can influence the learning process. The location of students' difficulties in learning English lies in abilities including writing ability and listening ability. The difficulty of spelling errors is 30%, vocabulary errors are 40%, listening errors are 10%, and language errors are 20%. This shows that the level of student ability has a role in the student learning process and can be one of the factors that influence the level of student academic achievement.

Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics

Linear algebra is one of the service mathematics courses that students in many programs take as part of their undergraduate study. Previous studies indicate that linear algebra courses are often challenging for undergraduate students, leading some to seek help from other resources, including online resources such as YouTube. Through a multiple case study, I focused on identifying the opportunities that YouTube resources could offer students to learn about eigenvalues and eigenvectors, which are among the key concepts in introductory linear algebra. I utilized a combination of APOS (Action-Process-Object-Schema) and Tall’s three worlds of mathematics to analyze two highly viewed YouTube videos on this topic. The two analyzed files had different emphases (one more on the embodied world, and the other on the proceptual-symbolic world), catering to students with different levels of understanding of linear algebra. The findings suggest that, overall, these resources could provide students with opportunities to learn about eigen theory in the embodied and proceptual-symbolic worlds, with more focus on action. Lecturers and teacher assistants could benefit from familiarizing themselves with these available resources and considering the possible integration of these resources into their teaching and/or support they provide for students to meet their academic needs and preferences.

Unequal Access to the Mathematics Course Ladder for Rural Students in the Southern States

A lack of access to a sequence of introductory to top-level curricula in rural schools has widened the achievement disparity between rural and urban students and influenced the number of college degree holders in rural areas. Recently, surging diversity and differentiation in income levels across nonurbanized areas can serve as determinants of the development of academically rigorous course pipelines in rural schools. This study examines differentiation in spatial access to the curriculum ladder for rigorous mathematics in three southern U.S. states during the 2017–18 school year: Alabama, Arkansas, and Mississippi. Policy variations in these states yield different effects on the sequence of rigorous mathematics courses in rural high schools. Given that the mathematics course pipeline reinforces college access, access to academically challenging courses likely outweighs the rural disadvantages of college readiness in non-urban students and the persistence of inequality in public education.

Designing and analysing a teaching proposal about linear algebra through the dialogue of two theories

In this paper we propose a new strategy of dialogue between theories, considering a semiotic cognitive analysis and a praxeological analysis. We examine the implementation of a teaching and learning sequence for introducing eigentheory in a linear algebra course taught during the first year of an engineering degree programme. Initially, the semiotic cognitive analysis based on the Action, Production and Communication space (APC) approach is used in the preliminary, a priori and in vivo phases of the didactic engineering process to propose a teaching strategy that incorporates a variety of semiotic resources. In a second moment, the praxeological analysis intervenes to reformulate the preliminary analysis and to progress on the consideration of a reference epistemological model about eigentheory in a first course of mathematics for engineers. This model is then used in the a priori and a posteriori analysis to integrate the semiotic and epistemological dimensions in the design and implementation of the teaching proposal. The results show the productivity of this new networking strategy and the complementarity of connecting the semiotic with the epistemological analysis.